Cameron was caught on camera Tuesday making the remarks to former New York mayor Michael Bloomberg in the United States, where he has been attending the UN General Assembly, AFP reported.
"The definition of relief is being the prime minister of the United Kingdom and ringing the Queen and saying: 'It's alright, it's OK.' That was something," Cameron said. "She purred down the line."
Cameron said he was "very embarrassed" and "extremely sorry" about what had happened. It is thought he will say sorry to the 88-year-old monarch at the next of their regular weekly meetings.
"It was a private conversation, but clearly a private conversation that I shouldn't have had and won't have again," he told reporters in New York.
"My office has already been in touch with the palace to make that clear and I will do so as well."
By constitutional convention, the queen must remain impartial over political issues such as the Scottish independence debate.
Royal officials had insisted she would not seek to influence last Thursday's closely-fought referendum but she did tell a well-wisher days before the vote: "I hope people will think very carefully about the future."
Scotland's First Minister Alex Salmond, who led the campaign for independence, was granted an audience with the queen at her Balmoral residence in the Scottish Highlands on Wednesday, officials said.
Salmond announced hours after the referendum result was announced that he would step down in November.